This thread explains clearly what the ShoddyBattle rating is and what you can use it for. It is displayed in your ladder record here:

As you can see, the rating has a lower value L and an upper value U. From these two values, you can find two very important numbers related to your rating, called xbar and sigma:

Code:

xbar = (U+L)/2
sigma = (U-L)/2

xbar is your mean, or average, rating. sigma is a number signifying the uncertainty of your rating. The larger sigma is, the more uncertain your average rating xbar is. For example, a rating displayed as being 1200-2000 is a much more uncertain rating than one displayed as being 1500-1700, even though both have the same average rating (xbar) of 1600.

The xbar value increases when you win games and decreases when you lose them. However, it does not always increase or decrease by the same amount, but proportional to how better or worse your opponent is. To put it in simple terms, if your opponent had a higher xbar value than yours before the start of the battle, your xbar value would increase by a lot if you win against him, but would only decrease by a little if you lose. Conversely, if your opponent had a lower xbar value than yours before the start of a battle, your xbar value would increase only slightly if you win against him, but would decrease drastically if you lose.

The sigma value always decreases whenever you battle, whether you win or lose. This is because the more you battle, the more the rating system gains accurate information of your Pokemon battling skills (or lack of) from the results of said battles, and hence the uncertainty of your xbar value decreases. On the other hand, if you stop battling, the sigma value would increase, indicating that your battling skills are now more uncertain, and this is where the volatility value comes in, since it is the value that governs the speed of your increase in sigma once a player stops battling.

The volatility is a measure of how consistent you are in your battles. If you tend to win against players you are expected to win against (i.e. having an xbar value lower than yours) and lose against players you are expected to lose against (i.e. having an xbar value higher than yours), your volatility would be low. A consistent player would thus have his sigma increase slower when he stops playing, because due to his previously consistent performances, his xbar value should become more uncertain at a slower rate.

Finally, a player is ranked on the ladder by his Conservative Rating Estimate (CRE). This is found as follows:

Code:

CRE = xbar - 4 * sigma

The Conservative Rating Estimate rewards players that have a high xbar (average rating) and low sigma (uncertainty of their average rating), by assigning them a larger number, and hence a higher rank on the ladder. However, while this ranking system is adequate, it has a few disadvantages, and should be replaced by a better one soon.

Earlier, I mentioned that a player is 'better' or 'worse' according to their corresponding xbar's and sigma's. In this final part of this thread, I shall provide a relatively simple approximation (compared to how it's actually calculated) to quantify this. It is written underneath in step-by-step form:

Step 1: Find the sum of the squares of both players' sigma's, add 100000 to this sum, and find the square root of the answer.

Step 2: Find the difference of the players' xbar's. Always subtract your xbar from your opponent's. Afterwards, multiply the result by 0.79 and divide by the number found in Step 1.

Step 3: Raise 10 to the power of the answer. Call this number G.

Step 4: For every game you win against the opponent, your opponent would win G games against you. Alternatively, the probability that you win against the opponent is 1/(1+G), while the probability that you lose against the opponent is G/(1+G).

Here's the equation for G in mathematical form:

Code:

G = 10^((OppXbar - YourXbar) * 0.79 / sqrt(100000 + YourSigma^2 + OppSigma^2))

Example: You have a rating of 1650 - 1738. Your opponent has a rating of 1580 - 1704.

YourXbar = (1738+1650)/2 = 1694

YourSigma = (1738-1650)/2 = 44

OppXbar = (1704+1580)/2 = 1642

OppSigma = (1704-1580)/2 = 62

Step 1: 44^2 + 62^2 = 1936 + 3844 = 5780. Adding 100000 to this we get 105780. The square root of this number is 325.238.

Step 2: 1642 - 1694 = -52. -52 * 0.79 = -41.08. -41.08 / 325.238 = -0.1263.

Step 3: 10^(-0.1263) = 0.7477. This is our G.

Step 4: For every game you win against the opponent, your opponent would win 0.7477 games. Alternatively, the probability that I win against the opponent is 1/(1+0.7477) = 57.22%, while the probability that my opponent wins against me is 0.7477/(1+0.7477) = 42.78%.